Question

The price of product A as a function of time is given by the function f(t). Similarly, the function g(t) represents the price of product B. We know that f is concave up and g is concave down. Explain what the concavity represents in the terms of the evolution of the price of A and B.

Answer 1

Answer:

Step-by-step explanation:

Recall that a function f is concave up if it's second derivative is positive and it is concave down if it's second derivative is negative. Recall that the second derivative tell us how the first derivative is behaving. Thus, if the second derivative is positive, then the first derivative is increasing as the time passes. If the second derivative is negative, that means that the first derivative is decreasing as the time passes.

Consider the product A with a price function that is concave up. This means that the first derivative is constantly increasing. This means, that if the price of the product A is decreasing, it will decrease less and less until it starts to increase. If on the contrary the price is already increasing, it will keep on increasing at a higher rate.

Consider the product B with a price function that is concave down. This means that the first derivative is constantly decreasing. So, if the price is increasing, it will increase less and less until it starts decreasing, or if it is already decreasing it will keep decreasing at a higher rate